New Zealand sent "both our love to Sir David's family, and our condemnation for this act of violence", she said.
Opposition leader Judith Collins described Amess' death as a "sad day for democracy".
"Shocking, and deeply sad news of the murder of Sir David Amess MP, while serving his constituency", Collins tweeted this morning.
"@NZNationalParty and I send our sincere condolences to Sir David's family, friends, colleagues, & constituents. A sad day for democracy."
Amess had been an MP since 1983. He's the second serving British MP to be killed in the past five years, following the murder of Labour MP Jo Cox in 2016.
The UK Home Secretary has ordered an urgent review of MPs' security, with counter-terror police are leading the investigation and detectives saying they're maintaining an "open mind" about the motive for the attack.